Graphics Reference
In-Depth Information
Figure 15.14.
Examples of blends.
Polyhedral blending
: Here objects are defined by polyhedra and one wants either
a polyhedral blending surface or a procedure that, via recursive subdivision, gener-
ates a polyhedral blending surface.
Volumetric blending
: This approach assumes that we have modeling system
based on solids. The system takes care of the blending and provides the user with
appropriate operations that carry out the blending automatically. Typically the
systems that support this are CSG or b-rep systems where the blending operations are
carried out via set operations on the solids. The blending here tends to be of a global
nature, whereas the other types of blending are more local, in that they apply only to
specific parts of an object.
At the computational level one can make some further distinctions. Is one dealing
with implicit or parametric surfaces? Are we using a subdivision algorithm? Are
we treating blending as a boundary value problem that is then solved numerically?
Additionally, [Wood87] separates blending operations into four types depending on
the extent of the blend, that is, how much or in what way the surfaces being blended
are modified. Figure 15.14 shows examples of the four types.
(1) There is no constraint and the blend has a global influence on the objects
(Figure 15.14(a)).
(2) The blend is constrained to lie in a volume (Figure 15.14(b)).
(3) The blend is constrained to lie in a given range in terms of distances from the
edges of surfaces (Figure 15.14(c)).
(4) The blend is constrained by specifying a minimum radius of curvature (Figure
15.14(d)).
We shall look first at several approaches to blending based on implicit surfaces
and begin with an example of
global blends
. Blinn ([Blin82]) was interested in dis-
playing molecules and wanted to get away from the “ball-and-stick” approach. He
wanted to blend the atoms. His idea was to think of an atom not as a sharply defined
ball but rather as a more nebulous object that had a high density near the center of
the object but whose density fell off to zero in an exponential fashion. The density
function for the atom with center at (x
1
,y
1
,z
1
) was therefore assumed to be of the form
(
)
=
e
ar
-
Dxyz
,,
,
where
